The purpose of this study was to design an alternative and robust method for estimation of glomerular filtration rate (GFR) in [99mTc]-diethylenetriaminepentaacetic acid ([99mTc] -DTPA renography with a reliability not significantly lower than that of the conventional Gates' method.

Methods: The method is based on renographies lasting 40 min in which regions of interest (ROIs) are manually created over selected parts of certain blood pools (e.g. heart, lungs, spleen, and liver). For each ROI the corresponding time-activity curve (TAC) was generated, decay corrected and exposed to a monoexponential fit in the time interval 10 to 40 min postinjection. The rate constant in min-1 of the monoexponential fit was denoted BETA. Following an iterative procedure comprising usually 5-10 manually created ROIs, the monoexponential fit with the maximum rate constant (BETAmax) was used for estimation of GFR.

Results: In a patient material of 54 adult subjects in whom GFR was determined with multiple or one sample techniques with [51Cr]-ethylenediaminetetraacetic acid ([51Cr]-EDTA) the regression curve of standard GFR (GFRstd) (i.e. GFR adjusted to 1.73 m2 body surface area) showed a close, non-linear relationship with BETAmax with a correlation coefficient of 95%. The standard errors of estimate (SEE) were 6.6, 10.6 and 16.8 for GFRstd equal to 30, 60, and 120 ml/(min·1.73 m2), respectively. The corresponding SEE values for almost the same patient material using Gates' method were 8.4, 11.9, and 16.8 ml/(min·1.73 m2).

Conclusions: The alternative rate constant method yields estimates of GFRstd with SEE values equal to or slightly smaller than in Gates' method. The two methods provide statistically uncorrelated estimates of GFRstd. Therefore, pooled estimates of GFRstd can be calculated with SEE values approximately 1.41 times smaller than those mentioned above. The reliabilities of the pooled estimate of GFRstd separately and of the multiple samples method are of the same magnitude. Therefore, [99mTc]-DTPA renography could replace the multiple samples method for GFR determination. In addition, the renography requires fewer resources from patient and staff and offers more clinical results as regards renal uptake function and renal outflow.

Gates' method (1) has been the most frequently used method for clearance estimation in radionuclide renography for the last two decades. In our department we started using the method for GFR estimation in [123I]-Hippuran renography (2,3). For the past 15 years we have used Gates' method for GFR estimation in [99mTc]-DTPA renography (3, 4) - although with several revisions of the method on more recent patient materials. Gates' method can also be applied for estimation of effective renal plasma flow in [99mTc]-MAG3 renography.

Gates' method estimates the clearance based on the ratio of the sum of the left and right renal counts rates at about 2 min postinjection to the estimated dose measured in kidney geometry in posterior view. This ratio will be called the total cleared renal fraction of cardiac output and denoted TCRF. Although the formula for TCRF is simple, the value of TCRF depends on several situations and on a number of measured and estimated parameters: a) net injected dose; b) the quality of the injection bolus; c) estimated kidney depths based on patient height and weight - particularly critical in obese patients; d) gamma camera sensitivity; e) linear attenuation coefficient of the radioisotope in the body at the level of the kidneys; f) the choice of the crucial background subtraction technique for calculation of the net renal count rates; and g) the size and shapes of the manually or automatically created whole kidney and renal background rois in the individual patient. Based on our long experience with Gates' method we do not regard it as a particularly robust method, but we use it in the daily routine when processing the renographies simply because the estimation of GFR requires practically no extra resources from either patient or staff.

In the past we have made several studies to design alternative, simple and robust methods for clearance estimation in radionuclide renography which were independent of Gates' method (3, 5-6). In these studies the time-activity curve over a certain part of the blood pool was analyzed by exposing it to monoexponential or biexponential curve fits. Taking into account our present knowledge and experience with these methods we have concluded: first, we did not properly account for the rapid equilibration of the radioactive indicator with an apparent perivascular distribution volume and, secondly, we did not properly account for the varying contributions of perivascularly distributed radioactive indicator within ROIs comprising even pronounced blood pools of the body such as the heart, spleen and liver.

The present study represents the final version of a preliminary study previously published as an abstract (7).

Materials and Methods

The imaging protocol of the [99mTc]-DTPA renography

A gamma camera (Genesys, Cirrus or Vertex, Philips Medical Systems, the Netherlands) with a 40-cm field of view and mounted with a low-energy high resolution parallel hole collimator was used. The patient was supine with the detector head opposite the kidney region from the dorsal side. Following a bolus injection in adults of about 150 MBq [99mTc]-DTPA (TechneScan® DTPA, Mallinckrodt Medical, The Netherlands) into the medial cubital vein, digital images were recorded for 40 min with 10 sec/frame. Images were recorded as 64 x 64 matrices in word mode with a 20% energy window around the [99mTc] photon peak.

Processing the [99mTc]-DTPA renography with respect to the rate constant method

A region of interest was created over a part of a blood pool (left ventricle, the whole heart, spleen, lungs, or liver). The corresponding time-activity curve was subsequently corrected for decay of the [99mTc] radioisotope. A monoexponential fit of the TAC with time constant BETA in min-1 was made in the time interval 10 min to 40 min postinjection. In the first iteration the parameter BETAmax was assigned the value of BETA (Figure 1).

Figure 1 - First iterative step with an ROI over the spleen. The TAC from 10-40 min is fitted with a monoexponential curve (shown in yellow). The rate constant BETA is 0.01187 1/min. BETAmax is 0.01187 1/min.

A second ROI over a vascular region was created. The above computational step was repeated for the new ROI yielding a new value of the time constant BETA. If BETA was greater than BETAmax, then BETAmax was assigned the value of BETA (Figure 2). This procedure was repeated about 5 to 10 times until it was no longer possible to find a ROI yielding a BETA greater than the current BETAmax (Figure 3).

Figure 2 - Second iterative step with an ROI over the liver. The TAC from 10-40 min is fitted with a monoexponential curve (shown in yellow). The rate constant BETA is 0.01177 1/min. BETAmax is 0.01187 1/min.

Figure 3 - Sixth iterative step with an ROI over the left ventricle. The TAC from 10-40 min is fitted with a monoexponential curve (shown in yellow). The rate constant BETAmax is 0.01354 1/min and this value was the maximum BETA value of 6 iterations. Therefore, BETAmax is 0.01354 1/min. This value yields a GFRstd equal to 78.9 ± 13.0 ml/(min·1.73 m2) (Eqs. 24-25).

The relationship between BETAmax and GFR

Define an optimum rate constant BETAopt by the ratio

BETAopt= GFR/PV

Eq. 1

where GFR is the glomerular filtration rate in ml/min and PV denotes the plasma volume in ml. The formula for BETAopt can be rearranged as follows:

BETAopt= [GFR · (PVroi/PV)] / [PV · (PVroi/PV)]

Eq. 2

or

BETAopt= GFRroi / PVroi

Eq. 3

where PVroi represents the plasma volume within the ROI over the blood pool and GFRroi represents a virtual GFR, i.e. the fraction of GFR which PVroi represents of PV.

The time-activity curve (TAC), which the gamma camera records within PVroi from 10 to 40 min postinjection and after decay correction can be expressed as function of time t:

TAC(t)= ALFA · exp(-BETA · t)

Eq. 4

where ALFA is a factor with the dimension of a count rate and BETA a rate constant in min-1.

If there was no exchange of [99mTc]-DTPA between the vascular and extravascular volumes, then BETA could be identified with BETAopt, i.e. the ratio GFR/PV. Let EVV denote the large extra-vascular volume.

Immediately following the radionuclide bolus injection a considerable part of [99mTc]-DTPA enters the EVV owing to the large differences in concentrations of [99mTc]-DTPA between PV and EVV. As in the GFR determination with [51Cr]-EDTA using the multiple samples technique, the concentration equilibrium of the radionuclide indicator between PV and EVV is attained after 3 hours. The extra-vascular distribution volume of [99mTc]-DTPA in the time interval from 10 min to 40 min postinjection will be called the perivascular distribution volume and denoted PVDV.

It is assumed that the net exchange of [99mTc]-DTPA between PV and PVDV from 10 min to 40 min postinjection is so small, that the decline in concentration of [99mTc]-DTPA in PV is approximately due to renal uptake alone. As a consequence of this, the rate constant BETA of a monoexponential fit to the TAC from 10 min to 40 min postinjection corresponds to the ratio for BETAopt in Eq. 3 as regards the numerator.

However, the inevitable presence of extra-vascularly distributed [99mTc]-DTPA within any ROI over a blood pool further complicates things. This extra-vascularly distributed [99mTc]-DTPA resides predominantly in the PVDV during the 40 min long renography. Let PVDVroi denote the perivascularly distributed [99mTc]-DTPA within a ROI over a blood pool.

Taking the above view points into consideration the rate constant BETA in Eq. 4 can be expressed as follows:

BETA= GFRroi / (PVroi + PVDVroi)

Eq. 5

Define the volume ratio (VR) as the ratio of PVDVroi to PVroi. Then Eq. 5 can be rewritten as

BETA= (1/(1 + VR)) · GFRroi / PVroi

Eq. 6

Equation 6 fully describes in mathematical terms the iterative nature of the procedure for determination of a value for BETA as close as possible to BETAopt in Eq. 3. The smaller VR is, the closer BETA will be to BETAopt. Hence, the purpose of the iterative method is not to find a ROI with a minimim size of PVDVroi but rather a minimum value for VR. This value will be denoted VRmin. Of course, when the iterations are stopped since a minimum value for VR has been obtained, this value corresponds to the above maximum BETA value (BETAmax).

The standard plasma volume can be estimated based on sex, height and weight in normal adults (8). If our patient material mentioned below is regarded as normal with respect to the plasma volume, the value for estimated PVstd can be calculated as 2283 ± 82 ml/1.73 m2 (mean ± 1 SD), i.e. with a coefficient of variation SD/mean of only 4%. Hence, it is reasonable to expect a fairly constant value for PVstd in Eq. 11. Equation 11 apparently establishes a direct proportionality between GFRstd and BETAmax. However, this does not hold true since it will be shown in the discussion section that VRmin is an increasing function of GFRstd.

Processing the [99mTc]-DTPA renography with respect to the Gates' method

Regions of interest were created around both kidneys and narrow perirenal background ROIs were drawn almost around the whole of the kidneys. The background ROIs were used for calculation of the net count rates in cps at 2 min postinjection for the left and right kidney (NCRl and NCRr). The count rates were corrected for the minimal decay of the [99mTc] radioisotope in the course of the 2 min. The kidney centre distances in dorsal projection of the left and right kidneys (KCDl and KCDr) were estimated based on patient's height and weight (9). Let Sgc denote the sensitivity in cps/MBq of the gamma camera at the surface of the collimator.

The kidney geometry factors for the measurements of the left and right kidneys (KGFl and KGFr) can be expressed as follows for the left kidney:

KGFl= TFit · Sgc · exp(-0.117 · KCDl)

Eq. 12

and for the right kidney as

KGFr= TFit · Sgc · exp(-0.117 · KCDr)

Eq. 13

The factor TFit represents the transmission factor of the imaging table. TFit was typically 0.90 for the three gamma cameras used in the study. The number -0.117 is the linear attenuation coefficient of [99mTc] in the body taking into account scattered radiation (4). The letters "exp" denote the exponential function.

The cleared renal fractions of the left and right kidneys at 2 min postinjection (CRFl and CRFr) are then calculated as

CRFl= NCRl / (KGFI · Q)

Eq. 14

and

CFRr= NCRr / (KGFr · Q)

Eq. 15

where Q is the net injected dose in MBq.

Finally, the total cleared renal fraction (TCRF) is calculated as

TCRF= CRFl + CFRr

Eq. 16

In Gates' method TCRF is used as an estimate of GFRstd.

Pooled value of GFRstd based on the rate constant and Gates' methods

Since the estimated values for GFRstd are statistically uncorrelated in the rate constant and Gates' method, a pooled estimate for GFRstd can be determined. Before a pooled estimated is calculated, a statistical test is performed with a view to deciding whether the two estimates are significantly different at the 5% significance level. If the two estimates are significantly different, no pooled estimate will be determined. In this situation it is concluded, that a least one of the two estimates is in error.

Let GFRbeta and GFRtcrf denote the estimated values of GFRstd in the rate constant and Gates' methods, respectively. Further, the corresponding standard deviations are denoted SDbeta and SDtcrf. The test variable SU measures the difference between the two estimates of GFRstd in standard units since SU is calculated as

SU= (GFRbeta - GFRtcrf) / (SDbeta2 + SDtcrf2)½

Eq. 17

If SU is above 2 or below -2 the conclusion is drawn that the two estimates are significantly different.

If they are not significantly different, the procedure for determination of a pooled estimate makes use of statistical weighting of the data, i.e. the weights of each of the two estimates is proportional to the inverse of the variance of each statistical variable. Let Wbeta and Wtcrf denote the weights of GFRbeta and GFRtcrf in the pooled estimate GFRpooled:

GFRpooled= Wbeta · GFRbeta + Wtcrf · GFRtcrf

Eq. 18

where

Wbeta= (1/SDbeta2) / (1/SDbeta2 + 1/SDtcrf2)

Eq. 19

and

Wtcrf= (1/SDtcrf2) / (1/SDbeta2 + 1/SDtcrf2)

Eq. 20

The standard deviation of the pooled variable (SDpooled) is calculated from Eq. 18 as

SDpooled= (Wbeta2 · SDbeta2 + Wtcrf2 . SDtcrf2)½

Eq. 21

A computational example illustrates the advantages of using a pooled estimate:

GFRbeta= 81.7 ± 13.1 ml/(min · 1.73 m2)

Eq. 22

and

GFRtcrf= 88.5 ± 14.6 ml/(min · 1.73 m2)

Eq. 23

Insertion of the variable values from Eqs. 22 and 23 into Eq. 17 yields SU equal to -0.35, i.e. there is no significant difference between GFRbeta and GFRtcrf. Insertion of the variable values from Eqs. 22 and 23 into Eqs. 18 and 21 gives GFRpooled equal to 84.7 ± 9.8 ml/(min · 1.73 m2). In comparison with Eqs. 22 and 23, the standard deviation of GFRpooled has been reduced with the factor 1.41 (i.e. the square root of 2) on the average. Hence, the use of a pooled estimate yields a more correct mean value for GFRstd with a standard deviation of the mean about 1.41 times smaller.

Patients

The patient material comprised 54 adult subjects (18 females, 36 males; age range 17-74 years, mean age 53 years). The subjects were selected from adult patients referred to our department for routine renography for various nephro-urological disorders in whom the glomerular filtration rate was determined simultaneously using the multiple samples or the one sample techniques with [51Cr]-EDTA. The majority of the GFR determinations employed the multiple samples technique, and all patients with an increased serum creatinine concentrations were examined using this method. In the multiple samples method 4 blood samples were drawn 3 hours postinjection with a time interval of 20 minutes. If the estimated endogenous creatinine clearance was below 30 ml/min, an additional blood sample was drawn 20 min after the 4th blood sample.

In two patients a part of the kidneys were outside the gamma camera field of view and, therefore, the patient material in Gates' method with determination of TCRF comprises only 52 patients.

Results

The rate constant method

Inspection of a plot of the data of GFRstd versus BETAmax revealed a distinct non-linear relationship between the two parameters. For that reason GFRstd was fitted to BETAmax with a monoexponential function including a constant term:

GFRstd= 93.94 · exp(49.32 · BETAmax) - 101.8

Eq. 24

with a standard error of estimate of GFRstd around the monoexponential fit

SEE = 962.7 · BETAmax

Eq. 25

Figure 4 shows the data of GFRstd and BETAmax for the patient material comprising 54 subjects including the regression curve and the 95% tolerance limits of GFRstd for a given value of BETAmax. A single data point is outside the tolerance limits.

Gates' method

Inspection of a plot of the data of GFRstd versus TCRF revealed a linear relationship between the two parameters. Linear regression of GFRstd versus TCRF yielded a correlation coefficient of 91% and the following regression line:

GFRstd= 13.61 · TCRF + 0.12

Eq. 26

with a standard error of estimate of GFRstd around the linear fit

SEE = 5.671 · (TCRF)½

Eq. 27

The intercept of the regression line in Eq. 26 is not significantly different from zero at the 5% significance level. Hence, TCRF represents an unbiased estimate of GFRstd.

Figure 5 shows the data of GFRstd and TCRF for the patient material comprising 52 subjects including the regression line and the 95% tolerance limits of GFRstd for a given value of TCRF. Three data points are outside, that is above, the tolerance limits.

Pooled estimates of GFRstd using the rate constant and Gates' methods

The patient material originally consisted of 52 subjects in whom both GFRbeta and GFRtcrf were determined. Pooled estimates of GFRstd were calculated according to Eq. 18. Four patients had to be excluded since they showed significantly different values of GFRbeta and GFRtcrf (Eq. 17). These four patients comprise the four patients with estimated GFRstd outside the 95% tolerance limits in Figs. 4 and 5. Having excluded these four patients, 48 patients remain in whom GFRstd and GFRpooled have been calculated.

Linear regression of GFRstd versus GFRpooled yields a correlation coefficient as high as 97% and the regression line:

GFRstd= 0.9961 · GFRpooled - 0.26

Eq. 28

with a standard error of estimate of GFRstd around the linear fit

SEE= 1.063 · (GFRpooled)½

Eq. 29

Figure 6 shows the data of GFRstd and GFRpooled for the patient material comprising 48 subjects including the regression line and the 95% tolerance limits of GFRstd for a given value of GFRpooled. No data points are outside the tolerance limits.

The slope and intercept of the regression line in Eq. 28 are not significantly different from unity and zero, respectively, at the 5% significance level. Hence, the regression line of GFRstd versus GFRpooled is not significantly different from the line of identity.

The separate reliabilities of the three estimates of GFRstd in comparison with the reliability of the multiple samples method.

The multiple samples method is known to have a reliability of about 10% for GFR of about 30 ml/min and about 7.7% for values exceeding 30 ml/min (10). For a considerably decreased, a moderately decreased and a normal GFRstd value of 30, 60 and 120 ml/(min · 1.73 m2), respectively, the SEE values of the rate constant method, Gates' method, and of GFRpooled were calculated from Eqs. 24-29. These SEE values include the reliabilities of the multiple samples method. Therefore they are regarded as the total SEE values.

Since the total variance of, for example, the rate constant method, is equal to the squared sum of the variances of the rate constant method separately and the multiple samples method separately, the reliability or SEE value of the rate constant method separately can be determined from the expression:

SEEbeta,sep = (SEEbeta,total2 - SEEmsm,sep2 )½

Eq. 30

where "tot" and "sep" refer to the total and separate SEE values, respectively. From equations similar to Eq. 30, the separate SEE values for Gates' method and GFRpooled were also calculated (Table 1).

Table 1 - The standard errors of estimate of estimated GFRstd in the multiple samples method with [51Cr]-EDTA (SEEmsm), the rate constant method (SEEbeta), Gates' method (SEEtcrf), and of GFRpooled (SEEpooled) for GFRstd equal to 30, 60 and 120 ml/(min · 1.73 m2). The total SEE values include the reliabilities of the multiple samples method, whereas the separate SEE values refer only to the method mentioned.

GFRstd ml/(min · 1.73 m2)

30

60

120

SEEmsm (separate)

3.0

4.6

9.2

SEEbeta (total)

6.6

10.6

16.8

SEEbeta (separate)

5.9

9.6

14.0

SEEtcrf (total)

8.4

11.9

16.8

SEEtcrf (separate)

7.8

11.0

14.1

SEEpooled (total)

5.9

8.3

11.7

SEEpooled (separate)

5.0

6.9

7.1

The following conclusions can be drawn from the table: a) The rate constant method possesses a reliability equal to or slightly better than that of Gates' method; b) The pooled GFR has a reliability about 30% better than that of the rate constant or Gates' methods; and c) The pooled GFR has a reliability slightly worse than that of the multiple samles method for moderately and considerably decreased GFRstd values but slightly better at normal glomerular filtration rates.

The apparent size of the perivascular distribution volume as function of GFRstd

Direct proportionality between GFRstd and BETAmax could be expected in Eq. 11 if the minimum volume ratio (VRmin) could be assumed to be constant from patient to patient. Fig. 4 clearly revealed that this assumption did not hold.

Solution of Eq. 11 with respect to VRmin gives:

VRmin= PVstd · BETAmax/GFRstd - 1

Eq. 31

VRmin is calculated for the patient material using estimatednormal values for PVstd based on sex, height and weight (8). A graph of VRmin versus GFRstd is shown in Figure 7. VRmin is near zero level for extremely decreased GFRstd values and increases to about 2.3 at high GFRstd values. In other words, the perivascular distribution volume 10-40 min postinjection in the [99mTc]-DTPA renography apparently increases with GFRstd. However, the relationship between the magnitude of [99mTc]-DTPA filtered into the lumen of the Bowman capsules and the diffusion (and possible filtration) of [99mTc]-DTPA from other capillary systems into the perivascular space is not clear to us.

On the apparent drawbacks of the rate constant method for estimation of GFRstd

It may be considered a drawback that our method is applied to [99mTc]-DTPA while this radioactive indicator in many places has been replaced by [99mTc]-MAG3 which yields better renal images since it has a renal clearance about 3 times that of [99mTc]-DTPA or GFR. However, since the most important parameter of renal function is the glomerular filtration rate, it can hardly be a drawback to use a radionuclide indicator for assessment of GFR which has a clearance almost identical to GFR itself.

The present version of the rate constant method requires that the renography lasts 40 min. This can be considered a drawback since the duration of a renography in most nuclear medicine departments is 20 min. In our department the renography lasts 20 min in the large patient group where renography is used for screening for renovascular hypertension. In the other large group with patients suspected of nephro-urological disorders the renography lasts 40 min. In our experience decreased renal function occurs more frequently in the latter patient group than in the hypertensive patient group. Hence, the rate constant method can be a valuable tool for alternative GFR estimation in routine renography in patients with nephro-urological disorders.

Using renographies lasting 40 min in nephro-urological patients there is a possibility for a more reliable quantification of renal outflow and, hence, for a more accurate distinction between a kidney with an obstructed and a non-obstructed dilated renal pelvis. Very decreased renal mean transit times cannot reliably be determined from renographies lasting 20 min (11-12).

Based on the above view points we recommend nuclear medicine departments to consider the advantages of using renographies lasting 40 minutes instead of the conventional 20 min, in particular in patients suspected of nephro-urological disorders.

Conclusion

This study offers a method for alternative estimation of GFRstd in [99mTc]-DTPA renography in comparison with the conventional Gates' method. The alternative rate constant method is as reliable as Gates' method but is not dependent on any measured or estimated parameters as is Gates' method. If the two statistically uncorrelated estimates of GFRstdare not significantly different, a pooled and unbiased estimate of GFRstd can be determined with values of SEE almost of the same magnitude as those of the reference method, i.e. the multiple samples method with [51Cr]-EDTA. If the two estimates are significantly different, the user is recommended to either choose the estimate based on the rate constant method or conclude that the two methods can yield no valid estimate.

Within an hour the [99mTc]-DTPA renography can yield a pooled estimate of total GFR, estimates of the single kidney GFR values and, in addition, information on renal sizes and renal outflow conditions. The multiple samples method yields only the total GFR and it requires a waiting and examination time for the patient of about 4-5 hours and an additional hour of laboratory work on the part of the technologist (preparation of the counting tubes with the plasma samples in the well counter and the subsequent processing of the count data in the computer). Therefore, GFR determination based on the pooled estimate during a 40 min [99mTc]-DTPA renography may replace the multiple samples or one sample methods for measuring GFR.